276 Mr. Power on Virtual Velocities. 
of the former. Let a, a, a’..... be the variations of the first 
class, and a, a, .... those of the second. Then 8, B, B’.... 
B, B,...-. being the corresponding spaces estimated in direction 
of the forces, and F, F’, F’,.... the forces requisite to maintain 
the equilibrium, we shall have, in consequence of what has 
been already proved, 
PB+PB+P"p'+....+P,B,4PB, 4+... V=o 
aig nip 
This equation is reduced by the hypothesis to 
Fa+F'd'+ Fa" +....=0. 
But a, a, «’.... being arbitrary and independent, we must have, 
separately, F=0, F’=0, F’=0, &c., and, consequently, the forces 
py pihpy ap alive | 
will be in equilibrium by themselves. 
J. POWER. 
Crare Hatt, 
March 19, 1825. 
